A boy is running on the plane road with velocity $v$ with a long hollow tube in his hand. The water is failing vertically downwards with velocity $u$. At what angle to the vertical, he must incline the tube so that the water drops enter it without touching its sides?
$\tan ^{-1}\left(\frac{v}{u}\right)$
$\sin ^{-1}\left(\frac{v}{u}\right)$
$\tan ^{-1}\left(\frac{u}{v}\right)$
$\cos ^{-1}\left(\frac{v}{u}\right)$
Two cars are moving in the same direction with the same speed $30 \,km/hr$. They are separated by a distance of $5\, km$, the speed of a car moving in the opposite direction if it meets these two cars at an interval of $4$ minutes, will be.......$km/hr$
A boat crosses a river with a velocity of $8\, km/h$. If the resulting velocity of boat is $10 \,km/h $ then the velocity of river water is...........$km/h$
A river is flowing from $W$ to $E$ with a speed of $5 \,m/min$. A man can swim in still water with a velocity $10\, m/min$. In which direction should the man swim so as to take the shortest possible path to go to the south.
A person is swimming with a speed of $10\, m /s$ s at an angle of $120^{\circ}$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is $'x'$ $m / s$. The value of $'x'$ to the nearest integer is ..............
A ship $A$ is moving Westwards with a speed of $10\, km h^{-1}$ and a ship $B$ $100\;km$ South of $A$, is moving Northwards with a speed of $10\, km h^{-1}$ .The time after which the distance between them becomes shortest, is ........ $hr$